In this paper, we examine the approximation of the probability density of a filtered signal envelope in the presence of phase noise. The probability density function (pdf) is of practical interest, especially for the performance evaluation of coherent optical systems employing envelope detection. We consider a few possibilities for approximate pdf construction,and develop simple, yet very accurate, expressions to describe the envelope of a filtered signal influenced by phase noise. To check the accuracy, we use the approximation for performance evaluation of a coherent optical frequency-shift keying (FSK) receiver, and compare the results with those obtained from existing methods.
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